A practical upshot of this will be PCs who are not deeply embedded/interconnected in the social aspects of the fiction.
The number of people I know, even the number of people who are my friends, would outstrip my capacity to note them all on a PC sheet. So if my PC knows only those people whom I write down, in advance, as part of the PC build process, the upshot is that my PC won't know many people.
That can be fine - it will create a feel about the PCs similar to Conan in The Tower of the Elephant (contrast, say, Conan in People of the Black Circle) - but obviously won't resolve the concern expressed upthread, of wanting players to have their PCs be more interconnected with the setting.
It feels like knowing people I didn't come up with during downtime or meet previously in play can still be a thing, without me as a player needing to come up with their names and traits as I'm playing.
"I go see if any of the usuals I play cards with are at the neighborhood bar." (as a character that might have mentioned looking for card games before or have cards on their list from a background)
"Are any of the neighborhood urchins I recognize around." (as a person who lives in the neighborhood)
"Does my usual armorer have any contacts who would know about the teamsters who bring in ore?" (as someone who has adventured for a while from a base town and wears armor)
"I go talk to someone at the brewers guild that I'm on good terms with" (as someone with brewing as a background)
"Do any of my neighbors have a son about the age of the person we're trying to impersonate?" (as someone living somewhere during downtime)
It feels kind of similar to:
"I use my old regiments battle cry." (ex-mercenary)
"I spin an upbeat song about a local legendary hero" or "I sing a popular local drinking song that would go over well with the men but not their wives" (bard)